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Question

Find the linear charge density if the intensity of the electric field produced by an infinite line charge at a distance of $$3m$$ is $$8\times10^5N/C$$.

A
$$10\ \mu C/m$$
B
$$1.33\ \mu C/m$$
C
$$2.55\ \mu C/m$$
D
$$2.66\ \mu C/m$$
Solution
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Correct option is B. $$1.33\ \mu C/m$$
Electric field due to infinite line charges at a distance d is given as:
$$E=\dfrac{\lambda}{2\pi\varepsilon_0d}$$

$$\lambda=2\pi\varepsilon_0dE$$
Here,
$$d = 3 cm = 0.03 m$$

$$E = 8 \times 10^4 N/C$$

$$\varepsilon_0 = \text{Permittivity of free space}$$
$$\dfrac{1}{4\pi\varepsilon_0}= 9 \times 10^9 N m^2 C^{−2}$$

$$\lambda=\dfrac{0.03\times8\times10^5}{2\times9\times10^9}$$

$$= 1.33 \mu C/m$$

Therefore, the linear charge density is $$1.33 \mu C/m$$.

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